We also tested the method proposed by Crespi and Boscardin
(2009) to perform model checking on multivariate outputs. It was
however found to be less efficient at discarding poor model fits than
the above approach, in the present case study. Note also that Perretti
et al. (2013c) mentioned that they performed some model-fit
diagnostics when applying parametric approaches, but without
further explanation. The fact that they were not able to detect model
misfit is likely due to the use of too liberal model checking tests. Such
too liberal tests are likely to stem from a direct interpretation of
posterior predictive p-Values or to the use of a set of summary
statistics that is not sufficient to properly assess model fit quality. This
should serve as a reminder that the power of model diagnostic
procedures should be tested with simulated datasets.